I don't expect bromide to do anything about this since the staining is likely just the coffee painting the gelatin, not so much silver fogging. Although the latter can also play a part of course. In that case KBr will help tone it down a little.
Btw, I have to admit I'm kind of the wrong audience for this; I never quite understood the attraction of these coffee developers. The way I see it they're fairly inefficient and the whole eco-story to surround them sounds fishy to me in the light of the quantity of instant coffee that's needed and the overall impact that has over its product life cycle. From a technical viewpoint it's very obvious that there are plenty of superior alternatives, many of which are very cost-effective and sometimes even relatively ecologically benign (instant Mytol etc.)